Subgroups — C₅₉×#21551 #28433660

Order 15104.

938 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2930	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1938	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1896	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₅₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#525	C₂²	1	2	yes	—
17	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#470	C₄	1	2	yes	complemented
19	C₅₉×#469	C₄	1	2	yes	complemented
20	C₅₉×#468	C₄	1	4	yes	complemented
21	C₅₉×#444	—	2	4	no	—
22	C₅₉×#436	—	2	4	no	—
23	C₅₉×#435	—	2	4	no	—
24	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#427	C₂²	1	1	yes	characteristic
27	C₅₉×#424	C₂²	1	2	yes	—
28	C₂×#104×C₅₉	C₂²	1	2	yes	—
29	C₂×#104×C₅₉	C₂²	1	2	yes	—
30	C₅₉×#416	C₂²	1	2	yes	—
31	C₅₉×#408	C₂²	1	2	yes	—
32	C₅₉×#407	C₂²	1	2	yes	—
33	C₅₉×#405	C₂²	1	2	yes	—
34	C₄×M₁₆×C₅₉	—	2	4	no	—
35	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#341	C₂²	1	2	yes	—
40	C₅₉×#339	C₂²	1	2	yes	—
41	C₅₉×#339	C₂²	1	2	yes	—
42	C₂×#41×C₅₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₅₉	—	2	1	no	—
44	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
45	#135×C₅₉	—	2	2	no	—
46	#135×C₅₉	—	2	2	no	—
47	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
49	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
50	#131×C₅₉	—	2	4	no	—
51	#131×C₅₉	—	2	4	no	—
52	C₂×M₁₆×C₅₉	—	2	2	no	—
53	C₂×M₁₆×C₅₉	—	2	2	no	—
54	C₂×M₁₆×C₅₉	—	2	2	no	—
55	C₂×M₁₆×C₅₉	—	2	2	no	—
56	C₂×M₁₆×C₅₉	—	2	2	no	—
57	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
58	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₅₉	D₄	1	4	yes	—
60	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
61	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₅₉	—	2	2	no	—
63	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
67	#123×C₅₉	—	2	2	no	—
68	C₂²⋊Q₈×C₅₉	C₂×C₄	1	4	yes	—
69	#121×C₅₉	C₂×C₄	1	4	yes	—
70	#120×C₅₉	—	2	2	no	—
71	C₄×D₄×C₅₉	—	2	4	no	—
72	#117×C₅₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	—	2	2	no	—
75	C₂×C₄²×C₅₉	—	2	2	no	—
76	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
78	#108×C₅₉	—	2	2	no	—
79	#108×C₅₉	—	2	2	no	—
80	#107×C₅₉	C₂×C₄	1	2	yes	complemented
81	#106×C₅₉	C₂×C₄	1	2	yes	complemented
82	C₄⋊C₈×C₅₉	—	2	4	no	—
83	#104×C₅₉	—	2	4	no	—
84	#104×C₅₉	—	2	4	no	—
85	#103×C₅₉	C₂×C₄	1	4	yes	complemented
86	#102×C₅₉	C₂×C₄	1	4	yes	complemented
87	C₂²⋊C₈×C₅₉	—	2	4	no	—
88	C₂²⋊C₈×C₅₉	—	2	4	no	—
89	#97×C₅₉	—	2	2	no	—
90	#97×C₅₉	—	2	2	no	—
91	#97×C₅₉	D₄	1	4	yes	complemented
92	C₄×C₈×C₅₉	—	2	2	no	—
93	C₄×C₈×C₅₉	—	2	2	no	—
94	C₄×C₈×C₅₉	—	2	2	no	—
95	C₂⁴×C₅₉	#41	1	1	yes	characteristic
96	#41×C₅₉	—	2	2	no	—
97	#41×C₅₉	—	2	2	no	—
98	#41×C₅₉	—	2	2	no	—
99	#41×C₅₉	—	2	2	no	—
100	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₅₉	—	2	2	no	—
102	C₂×D₄×C₅₉	—	2	4	no	—
103	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅₉	—	2	1	no	—
105	C₂²×C₄×C₅₉	—	2	1	no	—
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	2	4	no	—
110	C₂²×C₄×C₅₉	—	2	1	no	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	—	4	4	no	—
113	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₅₉	—	2	2	no	—
118	SD₁₆×C₅₉	—	2	4	no	—
119	D₈×C₅₉	—	2	2	no	—
120	M₁₆×C₅₉	—	2	4	no	—
121	M₁₆×C₅₉	—	2	4	no	—
122	M₁₆×C₅₉	—	2	8	no	—
123	M₁₆×C₅₉	—	2	2	no	—
124	M₁₆×C₅₉	—	2	2	no	—
125	M₁₆×C₅₉	—	2	2	no	—
126	M₁₆×C₅₉	—	2	2	no	—
127	M₁₆×C₅₉	—	4	4	no	—
128	C₂×C₈×C₅₉	—	2	1	no	—
129	C₂×C₈×C₅₉	—	2	1	no	—
130	C₂×C₈×C₅₉	—	2	1	no	—
131	C₂×C₈×C₅₉	—	2	1	no	—
132	C₂×C₈×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	2	2	no	—
134	C₂×C₈×C₅₉	—	4	4	no	—
135	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₅₉	#41	1	2	yes	—
143	C₂×C₈×C₅₉	#41	1	2	yes	—
144	C₄⋊C₄×C₅₉	—	2	4	no	—
145	C₄⋊C₄×C₅₉	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₅₉	—	2	4	no	—
147	C₂²⋊C₄×C₅₉	—	2	2	no	—
148	C₂²⋊C₄×C₅₉	—	2	4	no	—
149	C₄²×C₅₉	—	2	4	no	—
150	C₄²×C₅₉	—	2	1	no	—
151	C₄²×C₅₉	—	2	2	no	—
152	C₄²×C₅₉	—	2	1	no	—
153	C₄²×C₅₉	C₂×D₄	1	2	yes	—
154	C₄²×C₅₉	#41	1	2	yes	—
155	C₂³×C₅₉	—	2	1	no	—
156	C₂³×C₅₉	—	2	1	no	—
157	C₂³×C₅₉	—	2	2	no	—
158	C₂³×C₅₉	—	4	2	no	—
159	C₂³×C₅₉	C₄×D₄	1	2	yes	—
160	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
161	Q₈×C₅₉	—	2	2	no	—
162	Q₈×C₅₉	—	2	2	no	—
163	D₄×C₅₉	—	2	2	no	—
164	D₄×C₅₉	—	2	2	no	—
165	D₄×C₅₉	—	4	2	no	—
166	D₄×C₅₉	—	4	2	no	—
167	D₄×C₅₉	—	8	4	no	—
168	C₂×C₄×C₅₉	—	2	4	no	—
169	C₂×C₄×C₅₉	—	2	1	no	—
170	C₂×C₄×C₅₉	—	2	2	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	2	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	2	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	—	2	4	no	—
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	4	8	no	—
180	C₂×C₄×C₅₉	—	4	2	no	—
181	C₂×C₄×C₅₉	—	4	2	no	—
182	C₂×C₄×C₅₉	—	4	2	no	—
183	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₅₉	—	2	2	no	—
191	C₈×C₅₉	—	2	2	no	—
192	C₈×C₅₉	—	4	2	no	—
193	C₈×C₅₉	—	4	2	no	—
194	C₈×C₅₉	C₄×D₄	1	2	yes	—
195	C₈×C₅₉	C₄×D₄	1	2	yes	—
196	C₈×C₅₉	#121	1	4	yes	—
197	#21551	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₅₉	—	2	2	no	—
199	C₂²×C₅₉	—	2	4	no	—
200	C₂²×C₅₉	—	2	2	no	—
201	C₂²×C₅₉	—	4	2	no	—
202	C₂²×C₅₉	—	4	2	no	—
203	C₂²×C₅₉	—	4	4	no	—
204	C₂²×C₅₉	—	4	2	no	—
205	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₅₉	#525	1	1	yes	characteristic
207	C₂²×C₅₉	#529	1	1	yes	characteristic
208	C₄×C₅₉	—	2	4	no	—
209	C₄×C₅₉	—	2	2	no	—
210	C₄×C₅₉	—	4	2	no	—
211	C₄×C₅₉	—	4	4	no	—
212	C₄×C₅₉	—	4	2	no	—
213	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
215	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
216	C₄×C₅₉	#532	1	1	yes	characteristic
217	#3054	C₂×C₅₉	1	1	yes	characteristic
218	C₂×#444	C₂×C₅₉	1	1	yes	characteristic, complemented
219	#2930	C₂×C₅₉	1	2	yes	complemented
220	C₂×C₄×M₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
221	#1974	C₂×C₅₉	1	1	yes	characteristic, complemented
222	#1945	C₂×C₅₉	1	1	yes	characteristic, complemented
223	#1938	C₂×C₅₉	1	2	yes	complemented
224	#1896	C₂×C₅₉	1	2	yes	complemented
225	#1811	C₂×C₅₉	1	1	yes	characteristic, complemented
226	#1773	C₂×C₅₉	1	1	yes	characteristic, complemented
227	#1764	C₂×C₅₉	1	2	yes	complemented
228	C₂×C₅₉	—	2	1	no	—
229	C₂×C₅₉	—	2	1	no	—
230	C₂×C₅₉	—	4	2	no	—
231	C₂×C₅₉	—	8	2	no	—
232	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
233	C₂×C₅₉	#2956	1	2	yes	—
234	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic
235	C₂×#131	C₂²×C₅₉	1	2	yes	—
236	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
238	#525	C₂²×C₅₉	1	2	yes	—
239	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
240	#470	C₄×C₅₉	1	2	yes	complemented
241	#469	C₄×C₅₉	1	2	yes	complemented
242	#468	C₄×C₅₉	1	4	yes	complemented
243	#444	—	2	4	no	—
244	#436	—	2	4	no	—
245	#435	—	2	4	no	—
246	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
247	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
248	#427	C₂²×C₅₉	1	1	yes	characteristic
249	#424	C₂²×C₅₉	1	2	yes	—
250	C₂×#104	C₂²×C₅₉	1	2	yes	—
251	C₂×#104	C₂²×C₅₉	1	2	yes	—
252	#416	C₂²×C₅₉	1	2	yes	—
253	#408	C₂²×C₅₉	1	2	yes	—
254	#407	C₂²×C₅₉	1	2	yes	—
255	#405	C₂²×C₅₉	1	2	yes	—
256	C₄×M₁₆	—	2	4	no	—
257	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
258	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
261	#341	C₂²×C₅₉	1	2	yes	—
262	#339	C₂²×C₅₉	1	2	yes	—
263	#339	C₂²×C₅₉	1	2	yes	—
264	C₅₉	#21551	1	1	yes	characteristic, direct product factor, Sylow
265	C₂×#41	C₂³×C₅₉	1	2	yes	—
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
268	#135	—	2	2	no	—
269	#135	—	2	2	no	—
270	C₂×Q₁₆	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
271	C₂×SD₁₆	C₂×C₄×C₅₉	1	2	yes	complemented
272	C₂×D₈	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
273	#131	—	2	4	no	—
274	#131	—	2	4	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	C₂×C₄×C₅₉	1	2	yes	—
281	C₂×M₁₆	C₂×C₄×C₅₉	1	2	yes	—
282	C₂×M₁₆	D₄×C₅₉	1	4	yes	—
283	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
284	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
290	#123	—	2	2	no	—
291	C₂²⋊Q₈	C₂×C₄×C₅₉	1	4	yes	—
292	#121	C₂×C₄×C₅₉	1	4	yes	—
293	#120	—	2	2	no	—
294	C₄×D₄	—	2	4	no	—
295	#117	C₂³×C₅₉	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
301	#108	—	2	2	no	—
302	#108	—	2	2	no	—
303	#107	C₂×C₄×C₅₉	1	2	yes	complemented
304	#106	C₂×C₄×C₅₉	1	2	yes	complemented
305	C₄⋊C₈	—	2	4	no	—
306	#104	—	2	4	no	—
307	#104	—	2	4	no	—
308	#103	C₂×C₄×C₅₉	1	4	yes	complemented
309	#102	C₂×C₄×C₅₉	1	4	yes	complemented
310	C₂²⋊C₈	—	2	4	no	—
311	C₂²⋊C₈	—	2	4	no	—
312	#97	—	2	2	no	—
313	#97	—	2	2	no	—
314	#97	D₄×C₅₉	1	4	yes	complemented
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	2	2	no	—
318	C₂⁴	#41×C₅₉	1	1	yes	characteristic
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
338	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
340	Q₁₆	—	2	2	no	—
341	SD₁₆	—	2	4	no	—
342	D₈	—	2	2	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	2	8	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	4	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	4	no	—
358	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
359	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
360	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
365	C₂×C₈	#41×C₅₉	1	2	yes	—
366	C₂×C₈	#41×C₅₉	1	2	yes	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	C₂²×C₄×C₅₉	1	4	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×D₄×C₅₉	1	2	yes	—
377	C₄²	#41×C₅₉	1	2	yes	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₄×D₄×C₅₉	1	2	yes	—
383	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
407	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	C₄×D₄×C₅₉	1	2	yes	—
418	C₈	C₄×D₄×C₅₉	1	2	yes	—
419	C₈	#121×C₅₉	1	4	yes	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
428	C₂²	C₅₉×#525	1	1	yes	characteristic
429	C₂²	C₅₉×#529	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	4	no	—
435	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
436	C₄	C₄×#41×C₅₉	1	1	yes	characteristic
437	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
438	C₄	C₅₉×#532	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	2	no	—
443	C₂	C₄×#121×C₅₉	1	1	yes	characteristic
444	C₂	C₅₉×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂²×M₁₆×C₅₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₅₉×#444	C₂	semidirect
3. C₅₉×#2930	C₂	semidirect
4. C₂×C₄×M₁₆×C₅₉	C₂	semidirect
5. C₅₉×#1974	C₂	semidirect
6. C₅₉×#1945	C₂	semidirect
7. C₅₉×#1938	C₂	semidirect
8. C₅₉×#1896	C₂	semidirect
9. C₅₉×#1811	C₂	semidirect
10. C₅₉×#1773	C₂	semidirect
11. C₅₉×#1764	C₂	semidirect
18. C₅₉×#470	C₄	semidirect
19. C₅₉×#469	C₄	semidirect
20. C₅₉×#468	C₄	semidirect
47. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
48. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
49. C₂×D₈×C₅₉	C₂×C₄	semidirect
80. #107×C₅₉	C₂×C₄	semidirect
81. #106×C₅₉	C₂×C₄	semidirect
85. #103×C₅₉	C₂×C₄	semidirect
86. #102×C₅₉	C₂×C₄	semidirect
91. #97×C₅₉	D₄	semidirect
197. #21551	C₅₉	direct (N × H)
218. C₂×#444	C₂×C₅₉	semidirect
219. #2930	C₂×C₅₉	semidirect
220. C₂×C₄×M₁₆	C₂×C₅₉	semidirect
221. #1974	C₂×C₅₉	semidirect
222. #1945	C₂×C₅₉	semidirect
223. #1938	C₂×C₅₉	semidirect
224. #1896	C₂×C₅₉	semidirect
225. #1811	C₂×C₅₉	semidirect
226. #1773	C₂×C₅₉	semidirect
227. #1764	C₂×C₅₉	semidirect
240. #470	C₄×C₅₉	semidirect
241. #469	C₄×C₅₉	semidirect
242. #468	C₄×C₅₉	semidirect
264. C₅₉	#21551	direct (N × H)
270. C₂×Q₁₆	C₂×C₄×C₅₉	semidirect
271. C₂×SD₁₆	C₂×C₄×C₅₉	semidirect
272. C₂×D₈	C₂×C₄×C₅₉	semidirect
303. #107	C₂×C₄×C₅₉	semidirect
304. #106	C₂×C₄×C₅₉	semidirect
308. #103	C₂×C₄×C₅₉	semidirect
309. #102	C₂×C₄×C₅₉	semidirect
314. #97	D₄×C₅₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₉×#3054	2
C₂×C₅₉×#444	2
C₅₉×#2930	2
C₂×C₄×M₁₆×C₅₉	2
C₅₉×#1974	2
C₅₉×#1945	2
C₅₉×#1938	2
C₅₉×#1896	2
C₅₉×#1811	2
C₅₉×#1773	2
C₅₉×#1764	2
#21551	59

Subgroups — C59×#21551 #28433660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21551 #28433660